Finite Group Databasebeta

← #37548973

Subgroups — #37548973

Order 23168.

252 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042300C212yesmaximal, complemented
2#26042125C212yesmaximal, complemented
3#26042122C212yesmaximal
4C2×#19153772C211yesmaximal, characteristic
5C4⋊#13089685—22no—
6C22⋊#13089685C2214yes—
7#19153871—22no—
8C23×Dic181C411yescharacteristic
9#19153772—22no—
10#19153772—22no—
11C2×#15668428C411yescharacteristic
12C2×#15668428C2211yescharacteristic
13C2×C22⋊Dic181C2211yescharacteristic
14C2×C4×Dic181C411yescharacteristic
15C2×C4×Dic181C2211yescharacteristic
16C2×C22⋊C4×C181C411yescharacteristic
17C2×#13089685—24no—
18C22×Dic181—21no—
19C22×Dic181—21no—
20C22×Dic181—22no—
21C22×Dic181—22no—
22C22×Dic181C2×C411yescharacteristic
23C22×Dic181C2×C411yescharacteristic
24C22×Dic181C2×C411yescharacteristic
25C22×Dic181C2311yescharacteristic
26#15668428—22no—
27#15668428—22no—
28C22⋊Dic181—22no—
29C4×Dic181—21no—
30C4×Dic181—21no—
31C4×Dic181D412yes—
32C4×Dic181D412yes—
33C24×C181C2×C411yescharacteristic
34C22×C4×C181C2×C411yescharacteristic
35C22×C4×C181C2×C411yescharacteristic
36C22⋊C4×C181—22no—
37#13089685—44no—
38C2×Dic181—24no—
39C2×Dic181—24no—
40C2×Dic181—21no—
41C2×Dic181—21no—
42C2×Dic181—21no—
43C2×Dic181—21no—
44C2×Dic181—21no—
45C2×Dic181—41no—
46C2×Dic181—41no—
47C2×Dic181C22⋊C411yescharacteristic
48C2×Dic181C22⋊C411yescharacteristic
49C2×Dic181M1612yes—
50C2×Dic181C2×D412yes—
51C23×C181—21no—
52C23×C181—21no—
53C23×C181—41no—
54C23×C181—41no—
55C23×C181M1612yes—
56C23×C181C22×C411yescharacteristic
57C2×C4×C181—21no—
58C2×C4×C181—41no—
59C2×C4×C181—41no—
60C2×C4×C181C22⋊C412yes—
61C22×C181—21no—
62C22×C181—21no—
63C22×C181—22no—
64C22×C181—42no—
65C22×C181—42no—
66C22×C181—41no—
67C22×C181—41no—
68C22×C181C2×C22⋊C411yescharacteristic
69C22×C181C2×M1611yescharacteristic
70C22×C181C2×M1611yescharacteristic
71C4×C181—22no—
72C4×C181—41no—
73Dic181—21no—
74Dic181—21no—
75Dic181—22no—
76Dic181—22no—
77Dic181—41no—
78C2×C181—21no—
79C2×C181—21no—
80C2×C181—42no—
81C2×C181#40711yescharacteristic
82C2×C181#41011yescharacteristic
83C2×C181#41311yescharacteristic
84C181#146411yescharacteristic, complemented, Sylow
85#1464—1811nomaximal, Sylow
86C2×#117—1811no—
87#432—1812no—
88#324—1812no—
89#323—1812no—
90C23×C4—1811no—
91#117—3622no—
92#117—3622no—
93C2×C4⋊C4—1811no—
94C2×C4⋊C4—1811no—
95C2×C22⋊C4—1811no—
96C2×C22⋊C4#1062438211yescharacteristic
97C2×C42—1811no—
98C2×C42—1811no—
99C4⋊C8—3622no—
100C22⋊C8—1814no—
101#97—3622no—
102C24C2×#1062438211yescharacteristic
103C22×C4—3622no—
104C22×C4—3621no—
105C22×C4—3621no—
106C22×C4—3622no—
107C22×C4—1811no—
108C22×C4—1811no—
109C22×C4—1811no—
110C22×C4—1811no—
111C22×C4C2×#1062438211yescharacteristic
112C22×C4C2×#1062438211yescharacteristic
113C2×C8—3624no—
114C4⋊C4—3622no—
115C4⋊C4—3622no—
116C22⋊C4—22no—
117C22⋊C4—3622no—
118C42—3621no—
119C42—3621no—
120C42—1812no—
121C42—1812no—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#1566845912yes—
127C23C22×#1062438211yescharacteristic
128C2×C4—21no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—3624no—
132C2×C4—3624no—
133C2×C4—3621no—
134C2×C4—3621no—
135C2×C4—3621no—
136C2×C4—3621no—
137C2×C4—3621no—
138C2×C4—1811no—
139C2×C4—1811no—
140C2×C4—1812no—
141C2×C4—1812no—
142C2×C4—7241no—
143C2×C4—7241no—
144C2×C4C22⋊#1062438212yes—
145C8—7244no—
146C22—21no—
147C22—21no—
148C22—22no—
149C22—42no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22C2×C22⋊#1062438211yescharacteristic
154C22D181⋊M1611yescharacteristic
155C22C2×#1566845911yescharacteristic
156C4—22no—
157C4—41no—
158C4—3622no—
159C4—3621no—
160C4—3621no—
161C4—3622no—
162C4—7241no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#2604225011yescharacteristic
167C2#2604225911yescharacteristic
168C2#2604226611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC23×C181C22×C4
FrattiniC23C22×#10624382
FittingC2×C22⋊C4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC24×C181C2×C4
cosocleC22×Dic181C23
hypercenterC2×C22⋊C4#10624382
hypocenterC181#1464
LCSG ▷ C23×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #26042300C2semidirect
2. #26042125C2semidirect
84. C181#1464semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#260423002
#260421252
#260421222
C2×#191537722
#1464181